Disclosed herein are methods and systems that use life histories to determine component life, and more particularly to systems that use weighted least square regression to create a predictor for the expiration of replaceable components.
In image formation processing in an image forming apparatus represented by a printer system or the like, print processing is performed by using print materials such as a photoreceptor, a toner, and the like. Because these materials are reduced or degraded according to the use thereof, they are consumable items which require maintenance. These consumables may be arranged as unit called a cartridge, and if intended for replacement by the customer or machine owner, may be referred to as a customer replaceable unit (CRU). Examples of a CRU may include printer cartridge, toner cartridge, transfer assembly unit, photo conductive imaging unit, transfer roller, fuser or drum oil unit, and the like. It may be desirable for a CRU design to vary over the course of time due to manufacturing changes or to solve post-launch problems with the machine, the CRU, or a CRU and machine interaction. It is known to provide the CRU with a monitoring device commonly referred to as a CRUM (Customer Replaceable Unit Monitor). A CRUM is typically associated with a memory device, such as a ROM, EEPROM, SRAM, and other suitable non-volatile memory device or data collecting network system, with processing capabilities provided in or on the cartridge. Information identifying the CRU may be written on the EEPROM during manufacture of the CRUM. The printer system or the like updates the information in the memory element or other data collection system with monitored data to monitor the status of the replaceable module at the machine, at an external facility, or at the CRU.
The toner level in such an image forming apparatus is critical, and users appreciate knowing how much material is available. This is known as the remaining useful life of a consumable. A user may be distressed when finding out that the printer ran out of ink or toner in the middle of a print job. If the user was able to determine in advance that the useful life was relatively low, the user could take some steps to either more accurately estimate the possibilities of printing an entire print job using the amount of toner remaining in the currently installed toner cartridge at the printer, or could first go to the printer and install a new cartridge or ask someone at the network administrative level to replace the toner cartridge. Since most of the printers in the field are under some kind of service contract, the service providers would like to know exactly when they should ship the next consumable to the customer to replace the one in use without interrupting the printing service. A common method in predicting the remaining useful life of a consumable is by usage of a simple least square linear regression method. The simple least square regression method is a statistical technique which models the relationship between a set of dependent/response variables and a set of independent/predictor variables like the number of usage days or number of pages that can be printed until the life of the consumable is extinguished. The simple linear regression technique works well when the behavior of the dependent variables is regular (the usage is pretty much stable) and the variation is minor. The daily usage of the consumables, such as the daily usage of toner on office printing devices, is, however, by no means regular; printing is bursty and unpredictable on a daily basis. These problems reduce the ability of simple linear regression techniques to accurately predict the remaining life of toner cartridges and other consumables. Alternative approaches such as decision trees and classifiers to determine whether or not the level of a consumable is within a pre-specified reorder range have high scalability and implementation costs.
Statistically, the accuracy of results from any prediction model for consumable remaining life may depend on quite a few parameters such as the mean and the standard deviation/variance of the predicted time when life of the consumables ends, and the correlation coefficients between the usage of the consumable and the output of the service where, how and what the dependence are may depend on the consumable and how the model is created.